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Showing 1 to 6 of 6 for “"Jacobi Polynomials"”.
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Rodrigues Formula for Jacobi Polynomials on the Unit Circle
We begin by discussing properties of orthogonal polynomials on a Borel measurable subset of the complex plane. Then we focus on Jacobi polynomials and give a formula (analogous to the one discovered by R. D. Costin) for finding Jacobi polynomials on the unit circle. Finally, we consider some …
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Applied left-definite theory : the Jacobi polynomials, their Sobolev orthogonality, and self-adjoint operators.
… well known that, for –α, –β, –α – β – 1 ∉ ℕ, the Jacobi polynomials {Pn(α,β)(x)} ∞ n=0 are orthogonal on ℝ with respect to a bilinear form of the type(f,g)μ = ∫ℝfgdμ, for some measure μ. However, for negative integer parameters α and β, an application of Favard's theorem shows that the Jacobi …
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Discrete Harmonic Analysis Associated with Jacobi Expansions
… with the three-term recurrence relation for the Jacobi polynomials and we study some classical operators in Harmonic Analysis in this context. Particularly, we are interested in the heat and Poisson semigroups and in the maximal operators related to them, in the Riesz transforms, and in the …
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Efficient Techniques for Near-Field Computation and Subreflector Analysis
… computation, the series method of the modified Jacobi polynomials is employed. Advantages of this method over other existing methods are shown, and details for implementing the method for both planar aperture and reflector antennas are given.
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Discrete Harmonic Analysis related to classical orthogonal polynomials
… to the one associated with classical orthogonal polynomials. Its aim is the study of the discrete analogues of some classical operators in Harmonic Analysis. To be specific, the convergence problem of the multiplier of an interval for discrete Fourier series and the problem of the norm …
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Free Vibrations and Static Deformations of Composite Laminates and Sandwich Plates using Ritz Method
… method are chosen as a product of the classical Jacobi orthogonal polynomials and weight functions that exactly satisfy the prescribed essential boundary conditions while maintaining orthogonality of the admissible functions. For free vibrations of plates with curvilinear stiffeners, made …